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Hilbert space fragmentation provides a mechanism to break ergodicity in closed many-body systems. Here, we propose a realistic scheme to comprehensively explore this exotic paradigm on a Rydberg quantum simulator. We show that the Rydberg Ising model in the large detuning regime can be mapped to a generalized folded XXZ model featuring a strongly fragmented Hilbert space. The emergent Hamiltonian, however, displays distinct time scales for the transport of a magnon and a hole excitation. This interesting property facilitates a continuous tuning of the Krylov-subspace ergodicity, from the integrable regime, to the Krylov-restricted thermal phase, and eventually to the statistical bubble localization region. By further introducing nonlocal interactions, we find that both the fragmentation behavior and the ergodicity of the Krylov subspace can be significantly enriched. We also examine the role of atomic position disorders and identify a symmetry-selective many-body localization transition. We demonstrate that these phenomena manifest themselves in quench dynamics, which can be readily probed in state-of-the-art Rydberg array setups., Comment: 13 pages, 12 figures

Adiabatic time evolution of quantum systems is a widely used tool with applications ranging from state preparation through simplifications of computations and topological transformations to optimization and quantum computing. Adiabatic time evolution generally works well for gapped ground states, but not for thermal states in the middle of the spectrum that lack a protecting energy gap. Here we show that quantum many-body scars -- a particular type of highly excited states -- are suitable for adiabatic time evolution despite the absence of a protecting energy gap. Considering two rather different models, namely a one-dimensional model constructed from tensor networks and a two-dimensional fractional quantum Hall model with anyons, we find that the quantum scars perform similarly to gapped ground states with respect to adiabatic dynamics when the required final adiabatic fidelity is around 0.99. The maximum speed at which the scar state of the one-dimensional model can be adiabatically transformed decreases as a power law with system size, as opposed to exponentially for both generic thermal and disorder-driven localized states. At constant and very low ramp speed, we find that the deviation of the fidelity from unity scales linearly with ramp speed for scar states, but quadratically for gapped ground states. The gapped ground states hence perform better when the required adiabatic fidelities are very high, such as 0.9999 and above. We identify two mechanisms for leakage out of the scar state and use them to explain our results. While manipulating a single, isolated ground state is common in quantum applications, adiabatic evolution of scar states provides the flexibility to manipulate an entire tower of ground-state-like states simultaneously in a single system., Comment: 28 pages, 22 figures, v3: section III added

We show that the rainbow state, which has volume law entanglement entropy for most choices of bipartitions, can be embedded in a many-body localized spectrum. For a broad range of disorder strengths in the resulting model, we numerically find a narrow window of highly entangled states in the spectrum, embedded in a sea of area law entangled states. The construction hence embeds mobility edges in many-body localized systems. This can be thought of as the complement to many-body scars, an `inverted quantum many-body scar', providing a further type of setting where the eigenstate thermalization hypothesis is violated., Comment: 6 pages, 4 figures, v2: accepted version

We study the 3D Kitaev and Kitaev-Heisenberg models respectively on the hyperhoneycomb and hyperoctagon lattices, both at zero and finite-temperature, in the thermodynamic limit. Our analysis relies on advanced tensor network (TN) simulations based on graph Projected Entangled-Pair States (gPEPS). We map out the TN phase diagrams of the models and characterize their underlying gapped and gapless phases both at zero and finite temperature. In particular, we demonstrate how cooling down the hyperhoneycomb system from high-temperature leads to fractionalization of spins to itinerant Majorana fermions and gauge fields that occurs in two separate temperature regimes, leaving their fingerprint on specific heat as a double-peak feature as well as on other quantities such as the thermal entropy, spin-spin correlations and bond entropy. Using the Majorana representation of the Kitaev model, we further show that the low-temperature thermal transition to the Kitaev quantum spin liquid (QSL) phase is associated with the non-trivial Majorana band topology and the presence of Weyl nodes, which manifests itself via non-vanishing Chern number and finite thermal Hall conductivity. Beyond the pure Kitaev limit, we study the 3D Kitaev-Heisenberg (KH) model on the hyperoctagon lattice and extract the full phase diagram for different Heisenberg couplings. We further explore the thermodynamic properties of the magnetically-ordered regions in the KH model and show that, in contrast to the QSL phase, here the thermal phase transition follows the standard Landau symmetry-breaking theory., Comment: 13 pages, 12 figures